$file = "New Text Document.txt";
open (FILE, $file) or die "$!\n";
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I would venture the wild guess that there is no file New Text Document.txt in the directory from where you run your Perl program.

Personally, I would use the following idiom, which produces a somewhat nicer error message:

$file = "New Text Document.txt";
open my $fh, $file
    or die "Couldn't open '$file': $!\n";
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